Underground flow simulations using parallel finite element method

Computers & Geosciences - Tập 36 - Trang 161-166 - 2010
H. Mustapha1, A. Ghorayeb2, K.A. Mustapha3
1McGill University, Montreal, Canada, and Reservoir Engineering Research Institute, Stanford, USA
2TIMC Laboratory University, Grenoble, France
3Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

Tài liệu tham khảo

Albers, 2000, Average-case analyses of first fit and random fit bin packing, Random Structures Algorithms, 16, 240, 10.1002/(SICI)1098-2418(200005)16:3<240::AID-RSA2>3.0.CO;2-V Amir, L., Kern, M., Martin, V., Roberts, J., 2005. Domain decomposition for fractured porous media. In: Gmati, N., Jaoua, M., Moakher, M. (Eds.), Proceedings TamTam’05—2nd Conference on Trends in Applied Mathematics in Tunisia, Algeria, Morocco, Rabat, Maroc, pp. 295–300 [in French]. Baca, 1984, Modeling fluid flow in fractured porous rock masses by finite element techniques, International Journal for Numerical Methods in Fluids, 4, 337, 10.1002/fld.1650040404 Baker, 2006, An assumed partition algorithm for determining processor inter-communication, Parallel Computing, 32, 394, 10.1016/j.parco.2006.06.009 Beaudoin, A., De Dreuzy, J.R., Erhel, J., 2006a. A comparison between a direct and a multigrid sparse linear solvers for highly heterogeneous flux computations. In: Congrès Français de Mécanique CFM, Grenoble, France, poster [in French]. Beaudoin, A., De Dreuzy, J.R., Erhel, J., Mustapha, H., 2006b. Parallel simulations of underground flow in porous and fractured media parallel computing. In: Joubert, G., Nagel, W., Peters, F., Plata, O., Tirado, P., Zapata, E. (Eds.), Parallel Computing: Current and Future Issues of High-End Computing, Proceedings of the International Conference ParCo 2005, NIC Series, vol. 33, pp. 391–398. Bonnet, 2001, Scaling of fracture systems in geological media, Reviews of Geophysics, 39, 347, 10.1029/1999RG000074 Bour, 1998, On the connectivity of three dimensional fault networks, Water Resources Research, 34, 2611, 10.1029/98WR01861 Chavent, 1991, A unified physical presentation of mixed, mixed-hybrid finite element method and standard finite difference approximations for the determination of velocities in water flow problems, Advances in Water Resources, 14, 329, 10.1016/0309-1708(91)90020-O Chrisochoides, 2006, Parallel mesh generation, 237 Chrisochoides, 2003, Parallel Delaunay mesh generation kernel, International Journal of Numerical Methods in Engineering, 58, 161, 10.1002/nme.765 Falgout, 2005, Pursuing scalability for Hypre's conceptual interfaces, ACM Transactions on Mathematical Software, 31, 326, 10.1145/1089014.1089018 Galtier, J., George, P.L., 1997. Prepartitioning as a way to mesh subdomains in parallel. In: Proceedings of the Fifth International Meshing Roundtable, Pittsburgh, Pennsylvania, USA, pp. 107–122. Granet, S., Fabrie, P., Lemmonier, P., Quitard, M., 1998. A single-phase flow simulation of fractured reservoir using a discrete representation of fractures. In: Proceedings of the Sixth European Conference on the Mathematics of Oil Recovery, Peebles, Scotland, UK, pp. 1–10. Gupta, 1999, Pspases: an efficient and scalable parallel sparse direct solver, 1 Ivanov, 2006, Domain decomposition approach for automatic parallel generation of tetrahedral grids, International Mathematical Journal Computational Methods in Applied Mathematics, 6, 178 Kadow, C., Walkington, N., 2003. Design of a projection-based parallel Delaunay mesh generation and refinement algorithm. In: Proceedings of the Fourth Symposium on Trends in Unstructured Mesh Generation, Albuquerque, NM, USA, http://www.andrew.cmu.edu/user/sowen/usnccm03/agenda.html. Karimi-Fard, 2003, Numerical simulation of water injection in 2D fractured media using discrete fracture model, SPE Reservoir Evaluation and Engineering, 4, 117, 10.2118/83633-PA Karypis, G., Kumar, V., 1998. METIS: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. Report, Department of Computer Science/Army HPC Research Centre, University of Minnesota, Minneapolis, USA, p. 44. Kumar, 1994, Analyzing scalability of parallel algorithms and architectures, Journal of Parallel and Distributed Computing, 22, 379, 10.1006/jpdc.1994.1099 Meurant, G., 1999. Computer Solution of Large Linear Systems. North Holland, Amsterdam, 776 pp. Mustapha, H., 2006a. An adaptive method for flow simulation in three-dimensional heterogeneous discrete fracture networks. In: Proceedings of the International Conference on Scientific Computing (CSC), Nevada, USA, pp. 23–34. Mustapha, H., 2006b. Monte Carlo simulation of flow in three-dimensional discrete fracture networks. In: Proceedings of the World Congress in Computer Science (MSV), Computer Engineering, and Applied Computing, Las Vegas, USA, pp. 136–144. Mustapha, H., 2007. AM2FM: Automatic mesh generator for complex 2D discrete fractured media. Report, RERI (Reservoir Engineering Research Institute), Palo Alto, CA, USA, p. 41. Mustapha, H., Erhel, J., De Dreuzy, J.R., 2005. Heterogeneous fractured media: mathematical analysis and parallel computing. In: Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA), Las Vegas, USA, pp. 1031–1034. Mustapha, H., Ghorayeb, A., Mustapha, K., Saramito, P., in press. An efficient parallel mixed method for flow simulations. International Journal of Computer Mathematics. 10.1080/00207160802158728 Mustapha, 2007, A new approach to simulating flow in discrete fracture networks with an optimised mesh, SIAM Journal of Scientific Computing, 29, 1439, 10.1137/060653482 Noorishad, 1982, An upstream finite element method for solution of transient transport equation in fractured porous media, Water Resources Research, 18, 588, 10.1029/WR018i003p00588 Philip, 2005, Modeling coupled fracture-matrix fluid flow in geomechanically simulated fracture networks, SPE Reservoir Evaluation and Engineering, 8, 300, 10.2118/77340-PA Raviart, 1977, A mixed hybrid finite element method for the second order elliptic problem, Lectures Notes in Mathematics, 606, 292, 10.1007/BFb0064470 Saad, 1996 Wu, 2002, An efficient parallel-computing method for modeling nonisothermal multiphase flow and multicomponent transport in porous and fractured media, Advances in Water Resources, 25, 243, 10.1016/S0309-1708(02)00006-4 Wu, 2002, Massively parallel simulation of flow and transport in porous in variably saturated porous and fractured media, 289 Zhang, 2003, Massively parallel computing simulation of fluid flow in the unsaturated zone of Yucca Mountain, Nevada, Journal of Contaminant Hydrology, 62, 381, 10.1016/S0169-7722(02)00159-6